The processing of Mexican limes generates great amounts of peel as a byproduct. Lime peel is mainly rich in the flavonoid hesperidin, whose bioactivity is oriented mainly to cardiovascular diseases and cancer. The purpose of this work was to develop a green process for the extraction and purification of hesperidin from Mexican lime peel. The extraction of hesperidin was investigated on a laboratory scale by varying the solvent composition and the solid-to-solvent ratio. The best conditions (solid-to-solvent ratio of 0.33 g/mL and 60% ethanol) were used for the extraction of hesperidin in a pilot scale (Volume = 20 L). The kinetics of the extraction was studied to find the maximum hesperidin concentration at 100 min. The concentrated extract had a hesperidin content of 0.303 mg/mL. Next, a purification process using adsorption resins was assessed. Through static tests, it was determined that higher adsorption efficiencies were achieved with the EXA-118 resin and diluted extract (4:6 ratio with 10% DMSO). Finally, the adsorption of hesperidin from the diluted extract (hesperidin concentration of 0.109 mg/mL) was carried out at 25 °C in a column packed with 80 mL of EXA-118 resin. The mean recovery efficiency of hesperidin from the extract was almost 90%.